汽油机低摩擦系统优化及其对节能影响研究
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摘要
摩擦损失是发动机能量损耗的主要原因之一，降低发动机摩擦损失对于汽车节能减排具有重要意义。如何有效降低汽车发动机摩擦损失，已经成为各大汽车企业及研究机构的重要研究方向。本文通过数值模拟与试验相结合的方法，详细分析发动机结构参数对摩擦损失影响，利用系统摩擦学优化设计及类金刚石薄膜沉积相结合的方法，实现发动机降低摩擦损失及燃油消耗。
首先，基于流体动压润滑理论与多体系统动力学，建立发动机最重要摩擦副活塞-缸筒系统、活塞环-缸筒系统、曲轴-轴承系统摩擦学仿真分析模型，并在此基础上，开发发动机曲柄连杆机构摩擦学工程应用分析软件，分析摩擦副间油膜压力、最小油膜厚度、摩擦力及摩擦损失等摩擦性能参数。
利用摩擦学分析软件分析曲柄连杆机构及缸体结构参数对摩擦学性能的影响，分析结果如下：活塞裙部主副推力侧横向型面及纵向型线对摩擦损失都有明显影响，主推力侧影响略大。适当减小裙部横向型面，对油膜厚度没有明显影响；使裙部型线中凸点与活塞销中心线之间保持合理的距离，可以控制活塞的横向运动从而降低摩擦损失。适当调整活塞-缸筒之间间隙，可以降低摩擦损失，但对油膜有明显影响。活塞环高度及弹力对摩擦损失有明显影响，活塞环轴向高度对冲程中间点最小油膜厚度影响较大，但不改变流体润滑的性质，对上止点附近的最小油膜厚度影响不大，活塞环弹力降低对最小油膜厚度影响不大。轴承宽度、直径及曲轴轴承间隙对摩擦损失有明显影响，改变轴承结构后，随转速的降低，最大油膜压力升高。缸筒表面粗糙度对摩擦损失有重要影响。
在摩擦学仿真分析的基础上，对自主CA4GA发动机进行摩擦学系统优化设计。对曲柄连杆机构摩擦学系统优化设计包括：减少活塞裙部宽度，提高活塞裙部纵向型线中凸点；降低活塞环组弹力及高度，改变油环结构；降低曲轴主轴承宽度，增加曲轴主轴承间隙。对缸体摩擦学系统优化设计包括：通过调整珩磨设备加工工艺参数及更换珩磨刀具等措施，降低缸筒网纹表面粗糙度；减少缸盖螺栓力对缸筒变形影响，降低缸筒变形；减少曲轴箱内部缸间气体流动对摩擦损失影响，在缸体下部增加缸间通风孔，对缸体进行有限元结构强度分析。对配气机构摩擦学系统优化设计包括：降低气门弹簧预紧力及刚度，并进行配气机构动力学分析；在链条导轨表面开槽以减少润滑区接触面积，改进链条结构并降低表面粗糙度，降低链条张紧器刚度。
采用真空磁控溅射方法制备发动机DLC薄膜挺柱、活塞环及活塞销，分析DLC薄膜性能，DLC薄膜可以明显提高发动机零件表面硬度，通过适当过渡层可以使DLC薄膜与发动机零件间的结合力满足发动机使用要求。DLC薄膜在流体润滑条件下，对发动机零件摩擦系数几乎没有影响；在边界润滑及混合润滑状态下，可以明显降低发动机零件摩擦系数，且摩擦系数随着载荷的升高而降低。发动机零件沉积DLC薄膜后对表面粗糙度影响不大，可以明显提高发动机零件表面耐磨损性能。建立配气机构电动反拖试验台架分析DLC薄膜挺柱对配气机构摩擦损失的影响。发动机挺柱表面沉积DLC薄膜后，可以明显降低配气机构的摩擦损失，在转速范围内，平均降低10%左右。
利用拆除法反拖摩擦损失测试试验，测量低摩擦发动机与原机各系统及整机摩擦损失，分析发动机各零件结构参数及DLC薄膜对摩擦损失影响。在低负荷条件下，活塞裙部润滑接触面积及纵向型线的变化对摩擦损失影响不大，平均降低曲柄连杆机构摩擦损失3.6%；轴承宽度及轴承间隙的变化对摩擦损失影响不大，平均降低曲柄连杆机构摩擦损失2.3%；活塞环弹力对发动机摩擦损失有重要影响，平均降低曲柄连杆机构摩擦损失12.3%。综合对曲柄连杆机构进行系统摩擦学优化设计可以明显降低摩擦损失。曲轴箱内缸间气体流动对机械损失有明显影响，在缸壁上增加缸间通风孔可以有效降低发动机摩擦损失。气门弹簧弹力对配气机构摩擦损失有明显影响，平均降低配气机构摩擦损失2.3%；链条张紧器弹力对配气机构摩擦损失没有影响；链条结构及表面粗糙度对配气机构摩擦损失有明显影响，平均降低配气机构摩擦损失16.8%；链条导轨表面润滑接触区域对配气机构摩擦损失有明显影响，平均降低配气机构摩擦损失10%。对配气机构进行系统摩擦学优化设计，可以明显降低其摩擦损失。发动机摩擦学系统优化设计及DLC薄膜技术相结合的方法可以有效降低发动机摩擦损失，且在整个转速范围内都起作用，摩擦损失降低值恒定，不随转速变化。
利用台架性能试验测量低摩擦发动机与原机动力性能及燃油消耗性能，分析发动机摩擦损失对动力性能及燃油消耗性能的影响。对发动机整机运用系统摩擦学优化设计及DLC薄膜技术后，发动机整机摩擦损失降低17.1%。整机摩擦损失降低后，可以有效提升发动机动力性能，降低比油耗2.5%。
The friction loss is one of the main reasons for engine energy loss, and the reductionof engine friction loss is important to save automobile energy. Low friction technology ofengine has become an important research direction of the major auto companies andresearch institutions. Through the combination of numerical simulation and experimentalmethods, the effect of detailed engine structure parameters on the friction loss wasanalysed. Through the combination of system tribology design and diamond-like carbonfilms deposition methods, the engine friction loss and fuel consumption was reduced.
First, based on the hydrodynamic lubrication theory and multi-body system dynamics,the piston-cylinder system、piston ring-cylinder system and crankshaft-bearing systemtribological simulation analysis model was builded. On this basis, the engine tribologyengineering application analysis software was developed, which can analyze the frictionperformance parameters of the engine, such as the oil film pressure, minimum oil filmthickness and friction.
The effects of the crank-connecting rod mechanism and cylinder structure parameterson the tribological properties were analysed. The analysis results are as follows: the effectof the piston skirt horizontal surface and longitudinal line on friction loss is significant, theprimary thrust side impact slightly larger. Reducing the lateral surface of the skirt portion,there isn’t significant effect on the oil film thickness; kepping a reasonable distancebetween the higest point and the piston pin centerline, the lateral motion of the piston canbe controlled, and the friction loss wii be reduced. The clearance between the pistons withcylinder bore has influence on the friction loss, but there is a significant effect on the oilfilm. The effects of the height and elasticity of piston ring on friction loss is significant,there is a change of the minimum film thickness in the mid-stroke, there isn’t a change ofthe minimum film thickness on the TDC. The effect of piston ring stretch reducing on theminimum film thickness is significant. The effect of bearing width、 diameter andcrankshaft bearing clearance on friction loss is significant, after changing the bearing structure,, the maximum film pressure rise with the speed reduction. The effect of thecylinder bore surface roughness on friction loss is significan.
The next research content was tribological system optimization design for the CA4GAengine. The width of the piston skirts were reduced, the highest point of skirt profile linewas risen; the elasticity and height of the piston ring pack were reduced, the oil ringstructure was changed; the width of the crankshaft main bearings were reduced, theclearance of crankshaft bearings was increased. The tribological system optimizationdesign of cylinder included: reducing roughness of the cylinder bore; reducing distortion ofthe cylinder bore; increasing internal gas flow between the cylinder crankcase byventilation holes between cylinders, and analysis of the cylinder finite element structuralstrength was done. The design of the valve train tribological system optimization included:reducing valve spring preload and stiffness, and valve train dynamic analysis; chain guideslotted surface contact area to reduce the lubrication area;improving the chain structureand reducing the surface roughness; reducing the stiffness of the chain tensioner.
The engine DLC films tappets、piston rings and piston pins were prepared by vacuummagnetron sputtering method, the performance of the DLC films were analyzed, DLCfilms can be significantly improving the hardness of the engine parts surface, appropriatetransition layer can make the binding force between the DLC films and the engine parts.
In the fluid lubrication conditions, there is n’t effect of the friction coefficient of theengine DLC films parts; in the boundary lubrication and mixed lubrication conditions, itcan significantly reduce the friction coefficient of the engine parts, and the coefficient offriction is reduced as the load increases. The DLC films have no effect on the surfaceroughness of engine parts. But they can significantly improve wear resistance of engineparts surface. The motoring test bench was established to anaylsed valve train frictionlosses. The engine tappet deposited on the surface of the DLC film, it can significantlyreduce valve train friction losses in the rev range. It is10%lower on average.
Based on the engine friction strip-down tests, the friction losses of low friction engineand the original engine were measured, the friction loss of the structural parameters of theengine parts and the DLC films were analysed. Under low load conditions, the width andprofile line of piston skirt have no effect on friction losses, the average reduction of the friction loss is about3.6%; bearing width and the change of the bearing clearance has littleeffect on the friction losses, average2.3%; The effect of tension and height of piston ringson engine friction losses is important, average12.3%. Integrated crank linkage systemtribology optimized design can significantly reduce friction losses. Increased ventilationholes between cylinders can effectively reduce engine friction losses. Reducing valvespring tension can reduce valve train average friction losses2.3%; the chain tensionerelastic have no effect on valve train friction losses; changed chain structure and the surfaceroughness can reduce valve train friction losses16.8%; chain guide surface lubricatedcontact area can reduce valve train friction losses about10%. Tribology valve train systemoptimized design, can significantly reduce the friction losses. Engine tribological systemcombining the optimization of the design and the DLC films technology can effectivelyreduce engine friction losses.
Based on the performance test, the dynamic performance and fuel consumptionperformance of the low friction engine and the original engine was measured, and theeffect of engine friction loss on the fuel consumption was investigated. The test resultsshow that tribology structural optimization design and the diamond-like carbon (DLC)films can decrease mechanical friction loss of engine, it is decreased17.1%. The reducedfriction loss can effectively enhance engine performance, and the fuel consumption isdecreased2.5%.
首先，基于流体动压润滑理论与多体系统动力学，建立发动机最重要摩擦副活塞-缸筒系统、活塞环-缸筒系统、曲轴-轴承系统摩擦学仿真分析模型，并在此基础上，开发发动机曲柄连杆机构摩擦学工程应用分析软件，分析摩擦副间油膜压力、最小油膜厚度、摩擦力及摩擦损失等摩擦性能参数。
利用摩擦学分析软件分析曲柄连杆机构及缸体结构参数对摩擦学性能的影响，分析结果如下：活塞裙部主副推力侧横向型面及纵向型线对摩擦损失都有明显影响，主推力侧影响略大。适当减小裙部横向型面，对油膜厚度没有明显影响；使裙部型线中凸点与活塞销中心线之间保持合理的距离，可以控制活塞的横向运动从而降低摩擦损失。适当调整活塞-缸筒之间间隙，可以降低摩擦损失，但对油膜有明显影响。活塞环高度及弹力对摩擦损失有明显影响，活塞环轴向高度对冲程中间点最小油膜厚度影响较大，但不改变流体润滑的性质，对上止点附近的最小油膜厚度影响不大，活塞环弹力降低对最小油膜厚度影响不大。轴承宽度、直径及曲轴轴承间隙对摩擦损失有明显影响，改变轴承结构后，随转速的降低，最大油膜压力升高。缸筒表面粗糙度对摩擦损失有重要影响。
在摩擦学仿真分析的基础上，对自主CA4GA发动机进行摩擦学系统优化设计。对曲柄连杆机构摩擦学系统优化设计包括：减少活塞裙部宽度，提高活塞裙部纵向型线中凸点；降低活塞环组弹力及高度，改变油环结构；降低曲轴主轴承宽度，增加曲轴主轴承间隙。对缸体摩擦学系统优化设计包括：通过调整珩磨设备加工工艺参数及更换珩磨刀具等措施，降低缸筒网纹表面粗糙度；减少缸盖螺栓力对缸筒变形影响，降低缸筒变形；减少曲轴箱内部缸间气体流动对摩擦损失影响，在缸体下部增加缸间通风孔，对缸体进行有限元结构强度分析。对配气机构摩擦学系统优化设计包括：降低气门弹簧预紧力及刚度，并进行配气机构动力学分析；在链条导轨表面开槽以减少润滑区接触面积，改进链条结构并降低表面粗糙度，降低链条张紧器刚度。
采用真空磁控溅射方法制备发动机DLC薄膜挺柱、活塞环及活塞销，分析DLC薄膜性能，DLC薄膜可以明显提高发动机零件表面硬度，通过适当过渡层可以使DLC薄膜与发动机零件间的结合力满足发动机使用要求。DLC薄膜在流体润滑条件下，对发动机零件摩擦系数几乎没有影响；在边界润滑及混合润滑状态下，可以明显降低发动机零件摩擦系数，且摩擦系数随着载荷的升高而降低。发动机零件沉积DLC薄膜后对表面粗糙度影响不大，可以明显提高发动机零件表面耐磨损性能。建立配气机构电动反拖试验台架分析DLC薄膜挺柱对配气机构摩擦损失的影响。发动机挺柱表面沉积DLC薄膜后，可以明显降低配气机构的摩擦损失，在转速范围内，平均降低10%左右。
利用拆除法反拖摩擦损失测试试验，测量低摩擦发动机与原机各系统及整机摩擦损失，分析发动机各零件结构参数及DLC薄膜对摩擦损失影响。在低负荷条件下，活塞裙部润滑接触面积及纵向型线的变化对摩擦损失影响不大，平均降低曲柄连杆机构摩擦损失3.6%；轴承宽度及轴承间隙的变化对摩擦损失影响不大，平均降低曲柄连杆机构摩擦损失2.3%；活塞环弹力对发动机摩擦损失有重要影响，平均降低曲柄连杆机构摩擦损失12.3%。综合对曲柄连杆机构进行系统摩擦学优化设计可以明显降低摩擦损失。曲轴箱内缸间气体流动对机械损失有明显影响，在缸壁上增加缸间通风孔可以有效降低发动机摩擦损失。气门弹簧弹力对配气机构摩擦损失有明显影响，平均降低配气机构摩擦损失2.3%；链条张紧器弹力对配气机构摩擦损失没有影响；链条结构及表面粗糙度对配气机构摩擦损失有明显影响，平均降低配气机构摩擦损失16.8%；链条导轨表面润滑接触区域对配气机构摩擦损失有明显影响，平均降低配气机构摩擦损失10%。对配气机构进行系统摩擦学优化设计，可以明显降低其摩擦损失。发动机摩擦学系统优化设计及DLC薄膜技术相结合的方法可以有效降低发动机摩擦损失，且在整个转速范围内都起作用，摩擦损失降低值恒定，不随转速变化。
利用台架性能试验测量低摩擦发动机与原机动力性能及燃油消耗性能，分析发动机摩擦损失对动力性能及燃油消耗性能的影响。对发动机整机运用系统摩擦学优化设计及DLC薄膜技术后，发动机整机摩擦损失降低17.1%。整机摩擦损失降低后，可以有效提升发动机动力性能，降低比油耗2.5%。
The friction loss is one of the main reasons for engine energy loss, and the reductionof engine friction loss is important to save automobile energy. Low friction technology ofengine has become an important research direction of the major auto companies andresearch institutions. Through the combination of numerical simulation and experimentalmethods, the effect of detailed engine structure parameters on the friction loss wasanalysed. Through the combination of system tribology design and diamond-like carbonfilms deposition methods, the engine friction loss and fuel consumption was reduced.
First, based on the hydrodynamic lubrication theory and multi-body system dynamics,the piston-cylinder system、piston ring-cylinder system and crankshaft-bearing systemtribological simulation analysis model was builded. On this basis, the engine tribologyengineering application analysis software was developed, which can analyze the frictionperformance parameters of the engine, such as the oil film pressure, minimum oil filmthickness and friction.
The effects of the crank-connecting rod mechanism and cylinder structure parameterson the tribological properties were analysed. The analysis results are as follows: the effectof the piston skirt horizontal surface and longitudinal line on friction loss is significant, theprimary thrust side impact slightly larger. Reducing the lateral surface of the skirt portion,there isn’t significant effect on the oil film thickness; kepping a reasonable distancebetween the higest point and the piston pin centerline, the lateral motion of the piston canbe controlled, and the friction loss wii be reduced. The clearance between the pistons withcylinder bore has influence on the friction loss, but there is a significant effect on the oilfilm. The effects of the height and elasticity of piston ring on friction loss is significant,there is a change of the minimum film thickness in the mid-stroke, there isn’t a change ofthe minimum film thickness on the TDC. The effect of piston ring stretch reducing on theminimum film thickness is significant. The effect of bearing width、 diameter andcrankshaft bearing clearance on friction loss is significant, after changing the bearing structure,, the maximum film pressure rise with the speed reduction. The effect of thecylinder bore surface roughness on friction loss is significan.
The next research content was tribological system optimization design for the CA4GAengine. The width of the piston skirts were reduced, the highest point of skirt profile linewas risen; the elasticity and height of the piston ring pack were reduced, the oil ringstructure was changed; the width of the crankshaft main bearings were reduced, theclearance of crankshaft bearings was increased. The tribological system optimizationdesign of cylinder included: reducing roughness of the cylinder bore; reducing distortion ofthe cylinder bore; increasing internal gas flow between the cylinder crankcase byventilation holes between cylinders, and analysis of the cylinder finite element structuralstrength was done. The design of the valve train tribological system optimization included:reducing valve spring preload and stiffness, and valve train dynamic analysis; chain guideslotted surface contact area to reduce the lubrication area;improving the chain structureand reducing the surface roughness; reducing the stiffness of the chain tensioner.
The engine DLC films tappets、piston rings and piston pins were prepared by vacuummagnetron sputtering method, the performance of the DLC films were analyzed, DLCfilms can be significantly improving the hardness of the engine parts surface, appropriatetransition layer can make the binding force between the DLC films and the engine parts.
In the fluid lubrication conditions, there is n’t effect of the friction coefficient of theengine DLC films parts; in the boundary lubrication and mixed lubrication conditions, itcan significantly reduce the friction coefficient of the engine parts, and the coefficient offriction is reduced as the load increases. The DLC films have no effect on the surfaceroughness of engine parts. But they can significantly improve wear resistance of engineparts surface. The motoring test bench was established to anaylsed valve train frictionlosses. The engine tappet deposited on the surface of the DLC film, it can significantlyreduce valve train friction losses in the rev range. It is10%lower on average.
Based on the engine friction strip-down tests, the friction losses of low friction engineand the original engine were measured, the friction loss of the structural parameters of theengine parts and the DLC films were analysed. Under low load conditions, the width andprofile line of piston skirt have no effect on friction losses, the average reduction of the friction loss is about3.6%; bearing width and the change of the bearing clearance has littleeffect on the friction losses, average2.3%; The effect of tension and height of piston ringson engine friction losses is important, average12.3%. Integrated crank linkage systemtribology optimized design can significantly reduce friction losses. Increased ventilationholes between cylinders can effectively reduce engine friction losses. Reducing valvespring tension can reduce valve train average friction losses2.3%; the chain tensionerelastic have no effect on valve train friction losses; changed chain structure and the surfaceroughness can reduce valve train friction losses16.8%; chain guide surface lubricatedcontact area can reduce valve train friction losses about10%. Tribology valve train systemoptimized design, can significantly reduce the friction losses. Engine tribological systemcombining the optimization of the design and the DLC films technology can effectivelyreduce engine friction losses.
Based on the performance test, the dynamic performance and fuel consumptionperformance of the low friction engine and the original engine was measured, and theeffect of engine friction loss on the fuel consumption was investigated. The test resultsshow that tribology structural optimization design and the diamond-like carbon (DLC)films can decrease mechanical friction loss of engine, it is decreased17.1%. The reducedfriction loss can effectively enhance engine performance, and the fuel consumption isdecreased2.5%.
引文
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[5] International Energy Agency.World Energy Outlook2009[R].Paris：IEA,2009.
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[7]谢友柏.摩擦学的三个公理[J].摩擦学学报，2011,21（3）：161-165.
[8] Department of Education and Science.Lubrication(Tribology) Education andResearch[R].London：HMSO,1966.
[9] Kenneth Holmberg, Peter Andersson, Ali Erdemir. Global energy consumption dueto friction in passenger [J]. Tribology International,2012,47:221-234.
[10] Martin Skjoedt, Ryan Butts, Dennis N. Assanis. Effects of oil properties onspark-ignition gasoline engine friction [J]. Tribology International,2008,41：556–563.
[11]谢友柏.摩擦学科学及工程应用现状与发展战略研究-摩擦学在工业节能、降耗、减排中的地位与作用的调查[M].北京：高等教育出版社，2009.
[12] Richard Backhaus.Trends in powertrain technology[J], MTZ,2009,09(70)：4~9.
[13] Baglione M., M. Duty and G. Pannone. Vehicle System Energy AnalysisMethodology and Tool for Determining Vehicle Subsystem Energy Supply andDemand[C]. SAE paper2007-01-0398,2007.
[14] Bandivadekar. On The Road in2035: Reducing Transportation's PetroleumConsumption and GHG Emissions[R]. Massachusetts: MIT Laboratory for Energyand the Environment,2008.
[15] Baglione. Development of System Analysis Methodologies and Tools for Modelingand Optimizing Vehicle System Efficiency [D]. Michigan, University of Michigan,2007.
[16] Marcus Kennedy, Steffen Hoppe.Piston ring coating reduces gasoline enginefriction[J]．MTZ,2012,73(5):40-43.
[17] Dowson D.Man and Tribology [J]. Lubrication Technology,1977:99-102.
[18] Bowden F P, Tabor.The Friction and Lubrication of Solid [M].Oxford: ClarendenPress,1964.
[19]克拉盖尔斯基.摩擦磨损原理[M].北京：机械工业出版社，1982.
[20] V.L.Popov.Contact Mechanics and Friction Physical Principles and Applications[M]. Berlin: Springer,2009.
[21] Hitoshi Washizu, Shuzo Sanda, Shi-aki Hyodo, et al. Molecular DynamicsSimulations of elasto-hydrodynamic Lubrication and Boundary Lubrication forAutomotive Tribology [J]. Journal of Physics: Conference Series,2007,59(1):9-15.
[22] A P Panayi, H J Schock.Approximation of the integral of the asperity heightdistribution for the Greenwood-Tripp asperity contact model[J].EngineeringTribology,2008,222:165-169.
[23] Zheng ma, Naeim A.H. A Model for Wear and Friction in Cylinder Liners andPiston Rings [J].Tribology Transactions,2006,49:315-327.
[24] Samantha Uehara. Overview of New Surface Finishings for SI Bores [C].SAEPaper2007-01-2823,2007.
[25] Simon C.Tung, Michael L.McMillan.Automotive Tribology Overview of CurrentAdvances and Challenges for the Future [J].Tribology International,2004,37:517-536.
[26] Hugh Blaxill, Simon Reader, Stewart Mackay, et al. Development of a FrictionOptimized Engine [C].SAE Paper2009-01-1052,2009.
[27] Teru Ogawa, Tetsushi Suzuki. Reduction of Friction Losses in Crankcase at HighEngine Speeds [C].SAE Paper2006-01-3350,2006.
[28] Cleveland, A.E, Bishop, I.N. Several possible paths to improved part-load economyof park-ignition engines[C].SAE Paper150A,1960.
[29] Rogowski, A.R.Method of measuring the instantaneous friction of piston frictionand piston ring friction in a firing engine[C].SAE Paper379F,1961.
[30] Bishop, I.N. Effect of design variables on friction and economy[C].SAE Paper812A,1965.
[31] Richardson,D.E. Review of power cylinder friction for diesel engines [J]．ASME J.Eng. Gas Turbines and Power,2000,122：506-519.
[32] Taylor C M. Automobile engine tribology-design considerations for efficiency anddurability. Wear [J].1998,221:1~18.
[33] Staffan Johansson, Per H. Nilsson, Robert Ohlsson. Experimental frictionevaluation of cylinder liner/piston ring contact [J]. Wear,2011,271:625–633.
[34] O.Reynolds.On the Theory of Lubrication and its Application to Mr.BeauchampTower’s Experiments [J].Phil.Trans.roy.Soc,1886,117(1).
[35] Patir, N., Cheng, H.S. Application of Average Flow Model to Lubrication BetweenRough Sliding Surface [J]. ASME J Lubri Tech.1979,100(1):220-229.
[36] Patir, N., Cheng, H.S. An Average Flow Model for Determining Effect of ThreeDimensional roughness on Partial Hydrodynamic Lubrication [J]. ASME J LubriTech.1987,100(1):12-17.
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